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I am trying to prove that ifo(a)ando(b)are relatively prime, andab = ba, theno(ab) = o(a)o(b). I'd appreciate it if someone could give me a nudge in the right direction because I've spent almost 2 days on this now and I got nowhere. Which is rather annoying considering this is the first exercice in the chapter and the rest I did without a problem, so there must be something simple here that I'm missing.

I already know that if(m, n) = 1andm|kandn|kthenmn|k. I think I can use this to prove what I need, if I can only show thato(a)|o(ab)ando(b)|o(ab). (Because I've already shown thato(ab)|o(a)o(b), so provingo(a)o(b)|o(ab)will be enough.)

Thanks!

Chen

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# O(ab) when o(a) and o(b) are relatively prime

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